6 Arrays of 16 LED's controlled by Arduino

I know not to connect the Photodiode to pin 13 directly, I just had it like that as an example of what main components I will be using

Drawing circuits with faults in them is not good especially on this forum. OK so you knew what you meant but a beginner seeing that might have got the wrong idea.

I dont want to control each individual LED with drivers, I just want to control the whole set of them,

Most cubes use a technique called Charlieplexing.

This is where high low and off states are used on the lines. However, you still need a resistor somewhere in the path from high -> LED -> low.